While I’d link to think the “fusion power” has been driven into a corner I’d like to cut off its remaining escape route by applying pressure from the matter-antimatter on top and do so by looking at the enigmatic “intermix formula”.

Apparently, finding the right equation to mix matter and antimatter had already been a TOS issue in “The Naked Time”:

SPOCK: “Jim, there is an intermix formula. It's never been tested.” “It's a theoretical relationship between time and antimatter.””Stand by to intermix. I'll call the formulae in from the Bridge.”

In the first motion picture the energy from the matter-antimatter annihilation could instantly be applied to the impulse drive of new Enterprise (“Intermix set. Bridge, impulse power at your discretion.”), but the new warp engines obviously required a more sophisticated approach:

SCOTT: “Captain, it was the engine imbalance that created the wormhole in the first place. ...It'll happen again if we don't correct it.”
As to what created this „engine imbalance“ in the first place (Decker: “They went into antimatter imbalance”), Spocks talks about “engine design difficulties” but to remedy the situation seemed to be a question of fuel:
“I will now discuss these fuel equations with the Engineer.”

This then becomes the red thread for TNG, too. The intermix ratio, i.e. how many parts of matter you mix with antimatter, seems to become slowly but notoriously clear:

“Where No One Has Gone Before”:
PICARD: I don't understand your concern, Number One. They're not authorised to make any alterations in our engines, and according to Starfleet's report, they will simply test different ways of entering warp speed and different intermix formulas. What's the harm in that?
RIKER: It's the specs that Kosinski sent us. In my opinion, sir, they're gibberish.

„Booby Trap“:
LAFORGE: Matter-anti matter mixture ratio settings at optimum balance Reaction sequence corresponding to specified norms. Magnetic plasma transfer to warp field generators per programme specs. Commander, we should be going like a bat out of hell. (Aye. And if my grandmother had wheels, she'd be a wagon )

„Galaxy’s Child“:
LEAH: The matter-antimatter ratio has been changed. The mixture isn't as rich as regulations dictate.
LAFORGE: Experience has shown me that too high a ratio diminishes efficiency. I worked with the mixture until I got the right balance.

The TNG Technical Manual boiled it down / summed it up: the 1:1 ratio applies when traveling at warp 8 or faster. When traveling at lower speeds the intermix ratio is different - a ratio of 25:1 is only used when the core is online in an idle state, prior to full startup. At warp 1 it is tuned to 10:1, gradually changing until it reaches 1:1 at warp 8.

Three episodes prior to the production of “Skin of Evil” was “Coming of Age”, one of the few episodes sanctioned by Professor Krauss in his Physics of Star Trek because it was absolutely and scientifically correct and accurate (and possibly writer Sandy Fries included some self-critical intended pun).

COMPUTER: Last question on the hyperspace physics test. If the matter and antimatter tanks on a Galaxy class starship are nine tenths depleted, calculate the intermix ratio necessary to reach a starbase a hundred light years away at warp factor eight. Begin.
COMPUTER: Time elapsed. You now have one hour free before the next test.
MORDOCK: I must admit, Wesley, you have a very fast mind.
WESLEY: Once as I realised it was a trick question, there was only one answer.
MORDOCK: Yes, there is only one ratio with matter antimatter. One to one.

Almost looks like Riker was on to something when questioning Kosinski’s competence: "The equations he punched in were nonsense, just as we thought."

Admittedly, Leonard Nimoy, as chief science officer Spock, delivered some memorable lines in Star Trek regarding time travel, and no matter how hard I try, I find these difficult to forget.

Neither was his suggestion to recrystallize Klingon dilithium crystals in ST IV (i.e. by exposing these to gamma radiation which is the foremost product that comes from mass into energy conversion aka matter-antimatter annihilation or microscopic black holes used for warp drive) the kind of stuff you’d really like to write home about, especially not your physics teacher.

So what’s the story with the enigmatic “intermix formula” or “intermix ratio” the TNG producers hang on, even after such a noticable lecture in “Coming of Age”, after all, one of their own episodes!
Just ignore it and hope nobody will notice or are we looking at a different explanation?

This is either the third time (but anything than a charm) some Star Trek producers screwed up real science or a door to a logical conclusion:
“Something” is mixed, fused or integrated into the plasma energy resulting from the matter-antimatter annihilation and presumably originated from normal matter to explain such “intermix ratios” and/or “intermix formulas”.

Apparently dilithium crystals amplify and/or convert the energy channeled through these (even more enigmatic is how the warp engines actually use this energy to “warp” the “fabric of space” or space-time).

When a proton and an anti-proton (i.e. plus the neutrons = deuterium and anti-deuterium) annihilate each other, they produce heat, gamma radiation, electrons, positrons, and neutrinos.

It’s interesting to note that nuclear fusion (between a tritium and deuterium atom) produces compatible products: heat, gamma radiation and a neutron (fuse two hydrogen atoms into deuterium and you’ll get one antimatter electron / positron in the process).

If the dilithium crystals convert heat and gamma radiation from matter-antimatter annihilation into some form of “exotic” energy the “warp coils” require to do their job, it’s not farfetched to assume they’ll do the same or similar conversion with fusion energy and that’s where the “intermix formula” or “intermix ratio” starts to make sense, offering one or more of these explanations:

Matter-antimatter annihilation energy is joined by fusion energy for crystal conversion

Matter-antimatter annihilation energy is converted, fusion energy is added to the conversion product

Fusion energy is converted, matter-antimatter annihilation energy is added to the conversion product

Whatever the case, the warp drive requires at least the energy output of matter-antimatter and dilithium crystals.

__________________
"The first duty of every Starfleet officer is to the truth" Jean-Luc Picard
"We can't solve problems by using the same kind of thinking we used when we created them." Albert Einstein